Modelling asymmetrical and tail dependence for hydrological extremes in space and time

Temporal and spatial dependence is of great importance for hydrological investigations and specifically for extremes. The relationships between variables is often not symmetrical - high values are associated in a different manner then low ones. Copulas offer a possibility to model such dependences. Most well-known copulas offer a flexible modelling for pairs and cannot be generalized reasonably for higher dimensions. Vine copulas can be used to build higher dimensional complex dependences, but their construction is not straightforward. In this presentation a very flexible method to define multivariate copulas with asymmetrical dependence is presented. The method is based on a multilayer normal approach and allows a wide range of tail dependences. A generalization to time series and spatial random fields is also possible. Examples of groundwater contamination and precipitation fields illustrate the methodology.